Rb ultralong-range Rydberg molecules in magnetic and electric fields

We review the field of ultralong-range Rydberg molecules with a focus on recent developments. We briefly revisit the binding mechanism of Rydberg molecules based on electron-atom scattering and give an overview of experimental realizations in different ultracold atomic systems. However the main focus of the manuscript is on Rb2 Rydberg molecules. We discuss different angular momenta of the excited Rydberg states (S and D) and the interaction of the molecules with external electric and magnetic fields. Furthermore, we cover the transition from low atomic densities, where only a single atom is bound by a Rydberg electron, to high densities, where polyatomic bound states can be observed.